Ex. 4. Course E. by N. & N., distance 264 miles: find diff. of lat, and dep. Open Table I at 6 points, found at the bottom, and opposite the distance 264 stands departure 252.6, and difference of latitude 76.6.

Ex. 5. A ship sails N. 40° E., 50 miles: required the diff, of lat. and departure.

The course being less than 45°, is found at the top, and the distance being under 60 miles, is found in the left hand column; therefore on the page (56 Norie) is 40° at the top, and opposite to 50 in the distance column, marked Dist., is 38.3 under Lat., and 32'1 under Dep., the difference of latitude and departure required.

Ex. 6. A ship sails N. 64° W., 175 miles: required the diff. of lat. and departure. The course being more than 45°, is found at the bottom, in page 42, and opposite to the distance 175, is 767 over Lat., and 137.3 over Dep., which was required.

(a.) When there are tenths in the distance, in order to find diff. lat. and dep. in such case, take the distance as an entire number of miles, i.e., as a whole number, and find the corresponding diff. lat. and dep., from each of which cut off the right hand figure, or tenths, and remove the decimal point one place to the left hand, which will give the required diff. lat. and dep. in miles, and tenths of a mile. The tenths, however, must be increased by 1, if the figure cut off is 5, or upwards.

Ex. I. Course 3 points, distance 2013; required the diff. lat. and dep, corresponding thereto.

With course 3 points, and distance 2013, taken as 203, we get the diff. of lat. 156'9, dep. 128.8; now cut off the right hand figure of each (the 9 and 8), and shifting the decimal point one place to the left, we have diff. lat. 157, and dep. 12.9. It will be observed that the tenths are increased by 1, in each case, as the figures cut off in one case exceeds 5, and in the other amounts to 5.

Ex. 2. Required the diff. lat. and dep, corresponding to course 4 points, and dist. 24.3 miles.

With course 4 points, and dist. 24'3 (as 243 miles), we find diff. lat, 154°2, and dep. 187.8; hence we obtain, after dropping the tenths, and removing the decimal point in each one place to the left, 15'4, and 18.8, for the required quantities. The tenths in the dep., it will be observed, are increased by 1, since the figure dropped exceeds 5.

Ex. 3. N. 3 pts. W., and dist. 20.6 miles, give diff. lat. 17.1 N., and dep. 114 W. Ex. 4. N. 65° E,, and dist. 21°5 (as 215), give diff. lat. 90'9, and dep. 19489, which is diff. lat. 9'1 N., and 19'5 E. It will be observed that the tenths are increased by 1, in each case, as the figure dropped exceeds 5.

(b.) If the distance exceeds the limits of the Traverse Table, take the half, the third, &c., so as to bring it within the limits, taking care to multiply the corresponding quantities by 2, 3, &c.

Ex. 5. Let the course be 3 points, and distance 435: required the corresponding diff. lat. and dep.

435 divided by 3 gives 145.

Course 3 points, and dist. 145 give diff. lat. 116.5 and dep. 86.4

Diff. lat. 349'5 Dep. 259'2

If the distance had been 43'5, the diff. lat. would have been 350, and the dep. 25'9. (c.) But when the distance is between 300 and 600, we may take out diff. of lat. and dep. for 300, and for the excess of 300, take the sum of the quantities thus found, cut off the last figure and remove the decimal point as before.

Ex, 6. Course 5 points, and distance 526: required the corresponding diff. of lat. and departure.

Course 5 points, and dist. 300 give diff. lat. 128.3, and dep. 271*2

226 526

96.6 224'9

204'3

475'5

If the distance were 526, we should proceed as above, and then cutting off the last figure of each, and removing the decimal point one place to the left, the diff. of lat. is 2215, and dep. 47'6. The tenths are increased by 1, in each case, as the figure cut off in one exceeds 5, and in the other amounts to 5.

Given the difference of latitude and departure, to find the course and distance.

If the difference of latitude be greater than the departure, the course will be found at the top; but if the departure be the greater, the course will be found at the bottom of the tables.*

EXAMPLES.

Ex. I. A ship having sailed between the N, and E., until her difference of latitude is 199 miles, and her departure 144′6; required her course and distance.

In page 52 Norie, or page 474 Raper, these quantities will be found to correspond with 246 in the distance column, and with the angle 36° found at the top of the table; the course is, therefore, N. 36° E,, and distance 246 miles,

Ex. 2. A ship having sailed between the S. and W., until her difference of latitude is 40 miles, and her departure 139°4 miles: required the course and distance,

In page 32 Norie, or page 454 Raper, the course answering to latitude 40 miles, and departure 139.4 miles, corresponds with the angle 74°, at the bottom of the table, and opposite the distance 145 miles, in the bottom of the table; the course is, therefore, S. 74° W., and distance 145 miles, which was required.

*Always seek for the larger of the two given numbers in the column next the distance, viz., the column marked "lat." at the top of the page, until the smaller quantity be found opposite in the column marked dep. at the top; being careful to remember that when the dep. is more than the diff. of lat., the course will be at the bottom of the page.

TRAVERSE SAILING.

TRAVERSE SAILING is the case in plane sailing when the ship makes several courses in succession, the track being zigzag, and the direction of its several parts "traversing," or lying more or less athwart of each other. For all these actual courses and distances run on each, a single equivalent imaginary course and distance may be found, which the ship would have described had she sailed direct for the place of destination. Finding this course is called "Working a Traverse."

RULE XXXII.

1o. Draw out a form similar to that given in the example following. 2o. In the column headed Courses, enter each course in succession; and in column Dist., enter the distance run on each course.

3°. Take out of the Traverse Tables (Table I or II, Raper or Norie,) the difference of latitude and departure to each course and distance, and enter the latitude in column N. or S., and the departure in column E. or W., according to the name of the course.

Thus, if the course is S.E, by S. the difference of latitude must be entered in the column S., and the departure in the column E.; if the course is W. N. the difference of latitude must be entered in the column N., and the departure in the column W.; when the course is exactly North or South, there is no departure, and the whole distance is entered as difference of latitude in the corresponding column N. or S., as the case may be so when the course is due East or West, there is no difference of latitude, and the whole distance run is entered as departure in the E. or W. column. It may be advisable for a beginner, before he proceeds to take out the quantities from the Traverse Tables, to write a dash in all places not to be occupied by a difference of latitude or departure, in order to avoid writing a quantity in the wrong column. Such helps, however, are useless to an expert computer.

Ex. I. A ship from the Dudgeon light, in lat. 53° 19' N., sails S.S.E. E., 8 miles; E.N.E., 23 miles; N. W. by W. W., 36 miles; E N., 48 miles; and N.W. W., 46 miles required the latitude arrived at, also the course and distance made good.

DIFF. LAT,

DEPARTURE.

COURSES.

DIST.

N.

S.

E.

W.

Table I, Raper, and Table I, Norie.

(See Explanation below.)

Explanation. The courses and distances are entered in their proper columns, in the same order as they stand in the question: then in Traverse Table I, Norie or Raper, turn to the page with 24 points-which is found at the top, the course being less than 4 points-run the finger down the Dist. column till you come to 8, by the side of which stands 7'2 in Diff, lat. column, and 3'4 in Dep. column. Diff. lat. 7'2 is entered in the S. column, and Dep, 3'4 in the E. column, because the course is S, and E. (South and East). Next turn to the page of the Traverse Table with 6 points-found at the bottom, because more than 4 points-look for the distance 23, from the side of which take out Dep. 21°2, and Diff. lat. 8.8, which are entered under N. and E., because the course is N. and E. Proceed in a similar manner with the remaining courses.

The sum of the respective columns, N., S., E., and W., is next found, and the difference between the Northing, viz., 620, and the South, viz., 72, is taken, which leaves 54.8 N., which is the Diff. lat. made: the difference between the Easting 72'1, and West 67.3, leaves 4.8 E., departure.

We proceed in the next place to find the course and distance made good, thus:

Course N. 5° E.
Dist, 55 miles.

made good.

This is an illustration of the remark (see page 77) that when the diff. lat. is more than the dep., the course is less than 4 points, or 45°, and it is named from the N. towards the E., since the diff, lat. is N. and the dep. E.

Lat, left (or sailed from) Dudgeon light 53° 19' N.
Diff. lat. 54.8

Lat. in (or arrived at)

= 55 N.

Lat. in is found according to Rule XXII,

54 14 N.

page 53.

Ex. 2. A ship from Cape Espicheli, in lat. 38° 25′ N., sails as follows:-S.W. by W., 28 miles; W. by N., 55 miles: West, 47 miles; S.E. S., 25 miles; South, 101 miles; W. S., 72 miles: required the latitude in, also the course and distance made good.

DIFF. LAT.

DEPARTURE.

COURSES.

DIST,

We seek in the Traverse Table till the diff. of lat. 136.6, and dep. 180.5, are found opposite, each in their respective columns; the nearest to these are 180'5 and 136'0, which gives the course (at the bottom of page, dep. being the most) S. 53° W., and distance 22.6.

Lat. left

D. lat. 136.6

38° 25' N. = 2 17 S.

Lat.in (or arrived at) 36 8 N.

The lat. in is found according to Rule XXII, page 53.

Ex. 3. A ship from lat. 37° 24' S., sails the following true courses:-S.W. by S., 20 miles; West, 16 miles; N.W. by W., 28 miles; S.S. E., 32 miles; E.N.E., 14 miles; S.W., 36 miles; required the lat. in, also the course and distance made good.

We seek in the several pages of the Traverse Table II, for the diff, lat. 50'7, and dep. 507; the nearest found to these are diff. lat. 509, dep. 509, give course S. 45° W1, distance 72 miles.

The diff, lat, and dep, being of equal amount, the course is 45°, or 4 points, which illustrates the remark, page 49.

Lat. left
Diff. lat. 50'7

=

Lat, arrived at

37° 24' S. 51 S. 38 15 S.

The lat. sailed from being South, and the ship having sailed South, the ship has evidently increased her South lat., whence the sum of lat. from and d. lat. is taken to obtain lat. in.

Ex. 4. A ship from lat. 20° 56′ N., sails (all true courses) N.W. by N., 20 miles; S.W., 40 miles; N.E. by E., 60 miles; S.E., 55 miles; W. by S., 41 miles; E.N.E., 66 miles required the latitude in, also the course and distance made good.